3 Theories of the bid-ask spread Market Microstructure literature has identified three reasons for the existence of a bid-ask spread and other implicit transaction costs: 1. Order processing costs 2. Inventory Control 3. Asymmetric Information See Madhavan (2000), section 2 for a good review Textbook treatments of this material O Hara (1995), Chapters 2, 3 and 4 Lyons (2001), Chapter 4 De Jong and Rindi, Chapter 2, 3 and 4 3

4 Inventory models 4

5 Inventory control Important role of market makers: provide opportunity to trade at all times ( immediacy ) Market makers absorb temporary imbalances in order flow will hold inventory of assets inventory may deviate from desired inventory position risk of price fluctuations Market maker requires compensation for service of providing immediacy 5

11 Asymmetric information Traders on financial markets typically have differential information Usual distinction in microstructure literature: informed (I) and uninformed (U) traders U has only publicly available information I has public and some private information This has important implications for price formation: trading with potentially better informed party leads to adverse selection 11

15 Steps in the analysis of this model 1. derive distribution of asset s payoff conditional on public and private information 2. find demand schedule of traders by utility maximization 3. find equilibrium price by equating aggregate supply and demand Important result: equilibrium price reveals some of I s private information If U is smart (rational), he will take this information into account in his decisions Rational Expectations Equilibrium (REE) price price consistent with rational behaviour of U and I market clears 15

29 Summary of Kyle (1985) model informed traders will trade strategically, i.e. they condition trades on their private information maximize trading profits per trading round auctioneer will use an upward-sloping price schedule as a protection device against adverse selection net aggregate order flow reveals part of the private information order flow is informative, prices respond to trading after many trading rounds, prices converge to their full information (rational expectations) value prices are semi-strong form efficient (but not strong form efficient) 29

33 Informativeness of trades Essential idea: informed traders are more likely to buy when there is good news trade direction (buy or sell) conveys information about true value adverse selection problem for the market maker: informed traders only buy on one side of the market For example, buy trade will be interpreted as a good signal for the asset value; market maker updates expectations E[v buy] > E[v] Market maker will set zero-expected profit or regret-free prices ask = E[v buy], bid = E[v sell] 33

41 Main results of Glosten-Milgrom model endogenous bid-ask spread market is semi-strong form efficient prices are martingales with respect to public information with many trading rounds, prices converge to full information value 41

42 The Easley and O Hara (1987) model Extension of the Glosten-Milgrom model possibility that there is no information (event uncertainty) trades signal about quality of information (good or bad) but also about the existence of information (O Hara 3.4) choice of trade size (small or large) As in the GM model, uninformed trading is exogenous, split over small and large trade size Informed trader faces tradeoff: large size trade means higher profit, but also sends stronger signal of information 42

43 Possible outcomes Separating equilibrium: if large size is large enough, informed trader will always trade large quantity small trades only by U, hence no bid-ask spread for small size! Pooling equilibrium: I randomizes between small and large trades: hides some of his information to improve prices for large trades spread for small size smaller than spread for large size Important assumptions trading is anonymous informed traders act competitively: exploit information immediately 43

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